Last minute your best bet is CX. They consistently release award space last minute if seats are open in J and F.
You will need to use either the BA or JL website to search for award space. You'll have to use AS miles as AA doesn't permit routing to from India to US via Asia 1/2 (but Alaska does).
If you wanted to use AA miles, you could pick up a cheap flight MAA - BKK in Y and then use AA miles for either JL / CX / AA to route BKK - HKG/HND/NRT - SFO.
Also looks like you can get MAA - SIN - SFO on SQ PE for ~$800 - $1000 USD depending on dates.